The long-term cognition in musicians is unique. Music cognition is a relatively recent study of how learning music affects the development of the mind in areas such as memory, attention, performance, and comprehension. So much is being developed at once that there is a significant advantage in these areas of the brain in everyone that has even some musical learning versus people that have never studied. Of course, as a person becomes more dedicated in their music, the more advanced these areas of the mind are developed.
The learning of piano takes discipline. Piano players are applying themselves to an instrument that takes time to learn, because it is so complex and the knowledge required is so vast. A player learns to dedicate time into their craft, they learn the importance of dedication and for it they retain that new skill that can be displaced to other studies. It is no wonder that musicians have higher scores in standardized tests such as the SAT versus their non-musical peers. They are able to better study their other subjects.
An important part of music is performing, whether for a large audience or for few. Music is not meant to be solo- it is meant for an audience to enjoy. There is a reward that comes to piano players when they can share their talent with people. Confidence is built in piano players. Their emotional response to music is trained and they are better at grasping theories, music or otherwise. The whole mind takes part in creating the music- the logic and the emotional come together to create this intangible magic.